The family issued a statement saying that Cruz had been Jorge's friend since childhood and that Jorge was shot multiple times.
"Our family forgives the person who did this. One of Orlando's greatest legacies was to not hold grudges," it said.
Police and emergency officials swarmed the office of Environment and Natural Resources Ministry in the capital of Santo Domingo and barred entry as mourners gathered nearby.
Jorge's office was on the fourth floor of a building that also houses the Ministry of Tourism.
"We are troubled by the situation," Jorge's ministry said in a brief statement.
Bartolomé Pujals, executive director of the government's Cabinet of Innovation, wrote that he lamented the killing.
"His death is a tragedy," Pujals said. "We Dominicans have to come together to achieve a pact for peace and peaceful coexistence. No more violence."
Jorge, a lawyer, was appointed minister of the environment and natural resources in August 2020.